The present invention relates to radiography imaging and, more specifically, to a C-arm calibration method and apparatus for 3D reconstruction using 2D planar transformations for back-projection.
The following patent applications in the name of the present inventor and whereof the disclosure is hereby incorporated by reference to the extent it is not inconsistent with the present invention, are being filed on even date herewith and are subject to obligation of assignment to the same assignee as is the present application.
A C-ARM CALIBRATION METHOD FOR 3D RECONSTRUCTION;
APPARATUS FOR C-ARM CALIBRATION FOR 3D RECONSTRUCTION IN AN IMAGING SYSTEM;
APPARATUS FOR C-ARM CALIBRATION FOR 3D RECONSTRUCTION IN AN IMAGING SYSTEM UTILIZING A PLANAR TRANSFORMATION;
APPARATUS FOR PROVIDING MARKERS ON AN IMAGE, FOR USE IN CONJUNCTION WITH C-ARM CALIBRATION APPARATUS; and
A C-ARM CALIBRATION METHOD FOR 3D RECONSTRUCTION IN AN IMAGING SYSTEM.
Recent years have seen an increasing interest in tomographic reconstruction techniques using two dimensional detectors. These techniques are better known as cone-beam reconstruction techniques.
Helpful background information can be found in, for example, the following published materials. A. Feldkamp, L. C. Davis, L W. Kress. Practical cone-beam algorithm. J. Optical Society of. America. A 1984, 1, pp:612-619; Yves Trouset, Didir Saint-Felix, Anne Rougee and Christine Chardenon. Multiscale Cone-Beam X-Ray Reconstruction. SPIE Vol 1231 Medical Imaging IV: Image Formation (1990); B. D. Smith, xe2x80x9cImage reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methodsxe2x80x9d, IEEE Trans. MI4, 14-25, 1985; N. Navab et. al. Dynamic Geometrical Calibration for 3-D Cerebral Angiography. In Proceedings of SPIE Medical Conference, Newport Beach, California, February 1996; K. Andress. Fast Cone-Beam/Fan-Beam Reconstruction using the shear-scale-warp transformation. SCR Tech. Report, SCR-96-TR-565, 1996; and A Shashua. and N. Navab Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 18, No. 9, September 1996, pp. 873-883.
The following patent applications, whereof the disclosure is hereby incorporated by reference to the extent it is not inconsistent with the present invention, also provide background material for the present invention: CALIBRATION APPARATUS FOR X-RAY GEOMETRY, Ser. No. 08/576,736, filed Dec. 21, 1995 in the name of Navab et al.; CALIBRATION SYSTEM AND METHOD FOR X-RAY GEOMETRY, Ser. No. 08/576,718, filed Dec. 21, 1995 in the name of Navab et al.; METHOD AND APPARATUS FOR CALIBRATING AN INTRA-OPERATIVE X-RAY SYSTEM, Ser. No. 08/940,923, filed Sep. 30, 1997 in the name of Navab; and APPARATUS AND METHOD FOR POINT RECONSTRUCTION AND METRIC MEASUREMENT ON RADIOGRAPHIC IMAGES, Ser. No. 08/940,925, filed Sep. 30, 1997 in the name of Navab.
Feldkamp et. al., referred to in the afore-mentioned publications, proposed an approximate algorithm which has been widely accepted; Trouset et. al. proposed an algorithm based on Algebraic Reconstruction Technique (ART) that was based on two orthogonal Image Intensifier cameras carried by a specially tailored CT gantry; and an overview of cone beam reconstruction is provided in the work of Smith.
Feldkamp reconstruction technique is a generalization of the fan beam reconstruction extended to the third dimension. This method is based on filtered-backprojection. In this method, all the two dimensional projection images are first filtered, and then backprojected into the volume and combined.
In accordance with an aspect of the invention, it is herein recognized that theoretically, if the mapping between four non-collinear coplanar voxels and their pixel images is known, this 2-D transformation can be fully recovered without additional knowledge such as the X-ray projection geometry, X-ray source position, and image intensifier position. This approach for backprojection is of particular interest in conjunction with the present invention.
In the field of computed tomography, it is customary to use individual parameters of the geometry for backprojection. These parameters are computed at different calibration steps. Calibration apparatus and software that provides a transformation matrix relating each voxel in the world coordinate system to a point in the image has also been previously designed and used in order to compute a projection matrix. This matrix incorporates all the physical parameters involved in the 3-D to 2-D projection. These are the parameters that have been traditionally used in the backprojection step.
In the past, the number of the parameters used and computed in order to characterize both the geometry and the imaging parameters has been at least eleven parameters. It is herein recognized that theoretically six points including four coplanar points are sufficient for the calibration.
In accordance with an aspect of the invention, it is herein shown that one only needs to compute 8 parameters of a 2D planar transformation to calibrate the system and, in accordance with the present invention, only eight parameters of a 2D planar transformation are computed and this transformation is applied to get the backprojection onto one voxel plane. Three scale and shift parameters are then computed in order to backproject the data on to other parallel voxel planes; see the afore-mentioned K. Andress. Fast Cone-Beam/Fan-Beam Reconstruction using the shear-scale-warp Transformation. SCR Tech. Report, SCR-96-TR-565, 1996. However, these parameters result from the computed 2D transformation of the image using the four coplanar points and the position of the out of plane points of the calibration phantom. This procedure is described in more detail below.
In accordance with an aspect of the present invention, the transformation matrix has been successfully used in the backprojection step directly, without the need to know the individual physical parameters. This approach has been helpful in the following ways:
eliminating the need for running separate calibration steps;
providing a more accurate backprojection by computing all the parameters at once, keeping the overall projection error at a minimum in a least squared sense; and
formulating a voxel driven backprojection method based on homogeneous transformation matrices which resulted in an elegant and efficient algorithm.
If a 2D planar (or 2D to 2D or planar to planar) transformation is used instead of 3D-2D projection matrices the back-projection accuracy will be considerably increased. The calibration process also becomes easier. This is because the 2D transformation can be computed quite precisely with a small number of correspondences between coplanar model points and their images. This is not the case for the computation of the projection matrices.
Apparatus operating in accordance with the principles of the invention realizes a representation of the exact volume to be reconstructed or a volume which includes the volume of interest. The 2D transformation therefore backprojects the image directly into a plane inside the region of interest.
In accordance with an aspect of the invention, a C-arm calibration method for 3D reconstruction in an imaging system comprising an imaging source and an imaging plane, the method utilizes a planar transformation for relating voxels in a voxel space and pixels in the imaging plane, and comprises the steps of: defining a source coordinate system in reference to the imaging source.
In accordance with another aspect of the invention, defining a normal plane in the voxel space, not including the origin of the source coordinate system and being substantially normal to an optical axis from the source to the imaging plane; defining a relationship between the source coordinate system and another coordinate system, herein referred to as a world coordinate system, by transformation parameters; identifying pixel location coordinates for a respective pixel corresponding to each voxel by utilizing planar to planar transformation parameters; storing a value of a filtered image at the respective pixel location; accumulating contributions corresponding to a plurality of image projections so as to thereby reconstruct the each voxel; dividing the voxel space into a plurality of planes not parallel to the normal plane; back projecting an image of a plurality of pixels on the image plane onto a set of coplanar voxels defining one of the plurality of parallel planes; and defining a relationship in the source coordinate system between each of the plurality of pixels and corresponding ones of the coplanar voxels so as to obtain a 2-dimensional mapping between points on the one of the plurality of planes and pixels on the image plane.
In accordance with another aspect of the invention, the plurality of planes comprises 3 planes in addition to the normal plane.
In accordance with another aspect of the invention the plurality of planes comprises 3 planes forming, together with the normal plane, an intersection along one line.
In accordance with another aspect of the invention the plurality of planes and the normal planes are separated by consecutive angles of 45 degrees.
In accordance with another aspect of the invention, the plurality of pixels on the image plane comprises at least 4 pixels.
In accordance with another aspect of the invention a step is included of imaging 2 further voxels outside of the one of the plurality of parallel planes, whereby coordinate information is obtained defining a position for the source in terms of the 2-dimensional mapping.
In accordance with another aspect of the invention a step is included of deriving values for the transformation parameters from the coordinate information.
In accordance with an aspect of the invention, a C-arm calibration method for 3D reconstruction in an imaging system comprising an imaging source and an imaging plane, the method utilizes a planar transformation for relating voxels in a voxel space and pixels in the imaging plane, and comprises the steps of: defining a source coordinate system in reference to the imaging source; In accordance with another aspect of the invention defining a normal plane in the voxel space, not including the origin of the source coordinate system and being substantially normal to an optical axis from the source to the imaging plane; defining a relationship between the source coordinate system and another coordinate system, herein referred to as a world coordinate system, by transformation parameters; identifying pixel location coordinates for a respective pixel corresponding to each voxel by utilizing the planar to planar transformation parameters; storing a value of a filtered image at the respective pixel location; accumulating contributions corresponding to a plurality of image projections so as to thereby reconstruct the each voxel; dividing the voxel space into a plurality of planes not parallel to the normal plane; back projecting an image of a plurality of pixels on the image plane onto a set of coplanar voxels defining one of the plurality of parallel planes; and defining a relationship in the source coordinate system between each of the plurality of pixels and corresponding ones of the coplanar voxels so as to obtain a 2-dimensional mapping between points on the one of the plurality of planes and pixels on the image plane.
In accordance with another aspect of the invention, the plurality of planes comprises 3 planes in addition to the normal plane.
In accordance with another aspect of the invention the plurality of planes comprises 3 planes forming, together with the normal plane, an intersection along one line.
In accordance with another aspect of the invention the plurality of planes and the normal planes are separated by consecutive angles of 45 degrees.
In accordance with another aspect of the invention, the plurality of pixels on the image plane comprises at least 4 pixels.
In accordance with another aspect of the invention a step is included of imaging 2 further voxels outside of the one of the plurality of parallel planes, whereby coordinate information is obtained defining a position for the source in terms of the 2-dimensional mapping.
In accordance with another aspect of the invention a step is included of deriving values for the transformation parameters from the coordinate information.